These figures give the average number of quote arrivals on Reuters' screens, per five-minute intervals, from traders based in London and New York.8 Each location has activity beginning around 7:00 A.M. (local time) and lasting until about 6:00 P.M. (local time).9 Figure 2.2 integrates the London and New York data by converting the Eastern Standard Time (EST) New York times to Greenwich Mean Time (GMT) and plotting both figures 2.1a and figure 2.1b together. As noted by Bollerslev and Domowitz (1993, 1426), trading activity (as measured by the number of quote arrivals) in London begins high, declines until New York opens, then increases until the close of London trade. Activity in New York roughly follows that of London but continues strongly after the London close as New York becomes the major open market.

We wish to highlight several aspects of these data that make them excellent for studying models of asymmetric information. First, the interbank market is the closest to an ideal twenty-four-hour market of which we know. It is very liquid, especially by comparison with stock markets, in terms of both volume of trade and number of traders; individual traders have continuous access to the market via computer terminal; and some trader is active virtually around the clock (including the markets in the Far East). Second, the commodity is essentially the same in all markets: the deutsche mark and the dollar are the same irrespective of trader location, and settlement issues are trivial by comparison with, say, transactions on the New York Stock Exchange (NYSE) verThe data were kindly forwarded to us by Tim Bollerslev and Ian Domowitz. For details of the data capture, error screens, and data characteristics, see Goodhart (1990) and Goodhart and Figliuoli (1991).

8. We exclude quotes from Saturday and Sunday since there is almost no trading on these days (except the last hour on Sunday).

9. There are isolated quotes at times outside this interval, but they are negligible in frequency, and we ignore them in subsequent analysis. Note also that in London there is one period shortly before 6:00 P.M. (GMT) in which there are no quotes; this is reflected in figures 2.4a and 2.6 below by a "zero" spread at that time.

46 David A. Hsieh and Allan W. Kleidon Fig. 2.2 Number of quotes per five-minute interval, London and New York sus those on the International Stock Exchange (ISE) in London (see Burnham 1989,21).

Third, the facts of twenty-four-hour trading and the very size and nature of the foreign exchange markets suggest that standard models of asymmetric information may find it difficult to explain persistent temporal patterns since there may be less systematic private information in these markets compared with, say, a small NYSE-listed stock that has few followers. Lyons (1995) concludes that interpretation of "information" in the foreign exchange market must be broader than that in standard models of equity markets since there are no "insiders" in the foreign exchange market. Our discussion of learning models in section 2.3 below provides such a broader concept of information.

2.1.2 Results London and New York: Individual Markets We first document that volatility in the foreign exchange markets follows the same U-shaped pattern from the open to the close of trade as on, say, the NYSE. This is important because it is precisely this result that supports the conclusions of Admati and Pfleiderer (1988) and Subrahmanyam (1989) that there is heavy activity by informed traders at the open and close of trade on the NYSE, which results in the higher variances of returns at those times.

Return variances are calculated as follows. The day is first divided into oneminute intervals. At the end of each minute, the last quote (bid/ask) is averaged.

If no new quotes occur during that minute, the observation is deleted. Between 48 David A. Hsieh and Allan W. Kleidon two minutes (if both have quotes), the one-minute rate of return is computed as the discrete rate of change of the average bid/ask between the two minutes.

The standard deviation of each half hour (beginning at 7:30 A.M. local time) is computed as the standard deviation of these one-minute returns during the interval. For robustness, we present the medians of these half hourly standard deviations over all days in our sample.

Figures 2.3a and 2.

3b plot these average (median) standard deviations per half hour interval, from 7:30 A.M. (local time) to 6:00 P.M. for London and New York, respectively. The results are striking. The average variances are much higher at open and close in both markets than during other times of the trading day, confirming the apparent U shape in volatility that has been previously documented in other markets.10 Figures 2.4a and 2.4b present the average spreads (in pfennig per dollar) by minute over the trading periods indicated by trading activity in figures 2.1a and 2.1b above for London and New York, respectively. These figures confirm the general U-shaped pattern of spreads particularly documented in Bollerslev and Domowitz for smaller regional banks (1993, 1428ff.).

London and New York: Integrated Markets Figure 2.5 shows the standard deviations of both London and New York returns on the same (GMT) time scale. There appears to be no correspondence between the striking volatility patterns across these two markets, which are virtually instantaneously linked in terms of quote information.

Not surprisingly given the results in figure 2.5, figure 2.6 shows that changes in the bid-ask spread documented for London and New York separately do not provide any coherence when viewed at the same time across markets. While the average spread is roughly equal in London and New York when both markets are open, there is no apparent effect of the high spreads associated with the open or close of one market on the other market.

Table 2.1 presents a test of the difference in spreads between London and New York, by fifteen-minute intervals from noon GMT to 5:30 P.

M. GMT. The test assumes that samples are uncorrelated, with the result that the f-statistic for the difference of average spreads in each interval is downward biased if there is in fact positive correlation across the samples (which would be expected if information affected both sets of quotes throughout the day). The results confirm the impressions from figure 2.6 above and demonstrate that the (indicated) spreads in New York are consistently significantly higher than those in London, except for London close, when London spreads are higher

10. Note that, since we delete observations if no quote update occurs, and since we require consecutive observations to calculate a one-minute rate of return, there will be typically fewer observations for any given time interval than one observation per minute times the number of days in the sample. In particular, there are fewer observations in our sample at the open and close of trading than during periods of active trading. Table 2.3 below presents formal tests of the differences in variances.

than earlier in the London trading day and on average are higher than those in New York.

Table 2.2 tests for the difference between quote midpoints in London and New York, as opposed to the spreads.

Although table 2.1 above shows that the indicated spreads in New York are significantly higher than those in London except at London close, table 2.2 shows that this pattern does not carry over to mid-quotes. Although on average the London mid-quotes are greater than the New York mid-quotes, the difference is typically not statistically significant, at least assuming uncorrelated samples.

Table 2.3 examines the difference between mid-quote to mid-quote variances for London and New York, again by fifteen-minute intervals beginning at noon GMT.

The results from figure 2.5 above are supported in table 2.3.

From noon until 3:15 P.M., the variance in New York consistently exceeds that in London with the largest average variances in New York at the start of New York trading (although not all periods are individually significant at convenBid-Ask Spreads in Foreign Exchange Markets

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tional levels based on the conservative assumption of uncorrelated samples).11 However, the variance in London increases toward the close of London trading and significantly exceeds that in New York in the later part of the London trading period. The (conservative) ^-statistics are strongly significant at conventional levels in all periods between 4:00 P.M. and 5:30 P.M. (GMT) (the ^-statistics range from 2.64 to 5.53). Even in the last fifteen-minute interval (to 5:45 P.M.) in which there were only twelve observations in London, the ^-statistic is 1.73. Thus, these results clearly document a change in variance in one market that is not simultaneously observed in the other market.

The cross-market variance results in figure 2.5 and table 2.3 and the crossmarket spread results in figure 2.6 and table 2.1 constitute a challenge for standard asymmetric information models as applied to foreign exchange data.

11. The earliest intervals in New York (and the latest intervals in London) also have few observations (see n. 10 above).

54 David A. Hsieh and Allan W. Kleidon

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2.2 Current Asymmetric Information Models This section examines the standard asymmetric information literature as applied to the open and close of trade in foreign exchange markets. The general importance of asymmetric information has long been recognized. Bagehot (1971) argues that the marketmaker loses in trades with better-informed traders, with the result that trades with uninformed liquidity traders must make sufficient profit to cover those losses plus costs. This notion is formalized in subsequent work (see Admati 1991), the most relevant for our current purposes being Admati and Pfleiderer (1988) and Subrahmanyam (1989, 1991). Bollerslev and Domowitz (1993) explicitly interpret much of the foreign exchange behavior that we discuss in terms of the models of Admati and Pfleiderer and Subrahmanyam.12

12. Lyons (1993, 1995) develops microstructure models in the context of the foreign exchange market but does not examine cross-market data as in Bollerslev and Domowitz (1993).

55 Bid-Ask Spreads in Foreign Exchange Markets An initial problem with this literature is an inability of the theoretical model of Admati and Pfleiderer (1988), and the extension of this model by Subrahmanyam (1989, 1991), simultaneously to account for the observed empirical phenomena of volume, volatility, and bid-ask spreads on the NYSE (the market that these models were originally intended to explain).13 We then demonstrate that the cross-market foreign exchange results from section 2.1 above are inconsistent with standard asymmetric information models.

2.2.1 Admati and Pfleiderer (1988) A model of endogenous trading volume is provided by Admati and Pfleiderer (1988), who extend Kyle (1984). They assume three types of agents: informed traders, who will trade only on terms advantageous to them given their superior information; discretionary liquidity traders, who must trade over a given day but who choose when to trade during the day on the basis of trading costs (i.e., they trade in those periods of lowest cost); and nondiscretionary liquidity traders, who must trade at a given time during the day regardless of cost. In this model, trading costs arise solely because of the activity of the informed, whose profits are paid by the uninformed liquidity traders.

Given their assumptions, Admati and Pfleiderer show that it is possible to obtain concentrations of volume at arbitrary trading times because in equilibrium these high volume periods attract both informed traders and discretionary liquidity traders. The informed are attracted because there will be more uninformed liquidity traders behind whom they can camouflage their trades. The discretionary liquidity traders are attracted because, in this model, the increased activity of informed traders implies sufficiently increased competition among them that the cost of trading to the uninformed is lowered relative to other periods.

Admati and Pfleiderer relate their results to observed empirical behavior, especially to volume and variance at the open and close of a day's trading on the NYSE, and show "that the patterns that have been observed empirically can be explained in terms of the optimizing decisions of these traders" (1988, 4). Their primary motivation is the high volume and concurrent high variance at open and close. Volume is explained by their concentration equilibrium outlined above; high variance follows directly from the increased activity by informed traders at open and close since more (previously private) information is thus incorporated into prices.

2.2.2 Subrahmanyam (1989, 1991) The key result in Admati and Pfleiderer (1988)—namely, that increased activity by informed traders lowers the costs to the uninformed, who must pay the price of the presence of the informed—is not intuitively obvious. Subrahmanyam (1989, 1991) builds on the model of Admati and Pfleiderer and shows

13. Much of this discussion follows Brock and Kleidon (1992, sec. 4.3).

56 David A. Hsieh and Allan W. Kleidon that their result depends on the assumption of risk-neutral informed traders. If the informed traders are risk averse, then increased activity on their part can increase the trading costs of liquidity traders. Subrahmanyam (1989, 18) cites Foster and Viswanathan (1989) as showing that the adverse selection component of bid-ask spreads is highest at the beginning of the day, which "contrasts with the model of Admati and Pfleiderer [1988], which predicts that spreads should be lowest at the beginning of the day." Brock and Kleidon (1992, sec.

4.1) also provide evidence that appears inconsistent with the key result in Admati and Pfleiderer since spreads follow the same U shape as volume: highest volume is associated with highest, not lowest, costs.14 Subrahmanyam (1989) interprets this result as consistent with his extension of Admati and Pfleiderer to the case of risk-averse informed traders since then more trading by informed traders results in lower market liquidity and higher costs. To do this, he requires the additional assumption that "more individuals are informed at the beginning of the day than at other times during the day" (p.

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